|
|
A186459
|
|
Number of (n+1) X 7 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.
|
|
1
|
|
|
151, 197, 362, 673, 1061, 1693, 2377, 3677, 5073, 7977, 11533, 18221, 26957, 41729, 62105, 95205, 142645, 217581, 327233, 497481, 749885, 1137821, 1717565, 2603089, 3932825, 5956277, 9003685, 13630333, 20610673, 31193705, 47177837, 71391309
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>12.
Empirical g.f.: x*(151 - 105*x - 32*x^2 + 251*x^3 - 193*x^4 + 52*x^5 - 190*x^6 + 61*x^7 - 344*x^8 + 260*x^9 - 128*x^10 + 324*x^11) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Apr 17 2018
|
|
EXAMPLE
|
Some solutions for 3 X 7:
..1..1..0..0..0..0..1....0..1..0..1..0..0..0....1..1..1..1..1..1..1
..0..0..1..0..0..0..0....1..0..1..0..1..0..0....0..0..0..0..0..0..0
..0..0..0..1..0..0..0....0..1..0..1..0..1..1....0..0..0..0..0..0..0
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|